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Theorems · Theorem · group theory

AddCommGroup.modEq_comm

∀ {M : Type u_1} [inst : AddCommMonoid M] {a b p : M}, a ≡ b [PMOD p] ↔ b ≡ a [PMOD p]
Defined in
Mathlib.Algebra.Group.ModEq
Cited by
11 results in Mathlib
Foundations
Depth 9 from the axioms · uses propext
Assumes
AddCommMonoid
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AddCommGroup.neg_modEq_neg · cited by 2AddCommGroup.neg_modEq_negAddCommGroup.modEq_neg · cited by 2AddCommGroup.modEq_negeventuallyEq_toIcoDiv_nhds · cited by 2eventuallyEq_toIcoDiv_nhdseventuallyEq_toIocDiv_nhds · cited by 2eventuallyEq_toIocDiv_nhdsAddCommGroup.modEq_iff_eq_mod_zmultiples · cited by 1AddCommGroup.modEq_iff_eq…AddCommGroup.modEq_iff_intModEq · cited by 1AddCommGroup.modEq_iff_in…AddCommGroup.modEq_nsmul_cases · cited by 1AddCommGroup.modEq_nsmul_…toIcoMod_eventuallyEq_toIocMod · cited by 0toIcoMod_eventuallyEq_toI…AddCommGroup.modEq_zero_iff_eq_zsmul · cited by 0AddCommGroup.modEq_zero_i…AddCommGroup.sub_modEq_iff_modEq_add · cited by 0AddCommGroup.sub_modEq_if…AddCommGroup.sub_modEq_iff_modEq_add' · cited by 0AddCommGroup.sub_modEq_if…AddCommMonoid · cited by 12281AddCommMonoidAddCommGroup.ModEq · cited by 107AddCommGroup.ModEqAddCommGroup.ModEq.symm · cited by 2ModEq.symmAddCommGroup.modEq_commCITED BYCITES

Cites3

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Cited by11

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